Question

If y =-1/3 is a zero of a polynomial P(y) = 27y3 – ay2 – y +3, then find the value
of ‘a’.

Answer 1

Answer:

given

$y = - 1 \div 3 \\ = 27 {y}^{3} - a {y}^{2} - y + 3 = 0 \\ p( - 1 \div 3) = 27 {( - 1 \div 3)}^{3} - a {( - 1 \div 3)}^{2} - ( - 1 \div 3) + 3 = 0 \\ 27( - 1 \div 27) - a \times (1 \div 9) + (1 \div 3) + 3 = 0 \\ - 1 + 3 + (1 \div 3) - (a \div 9) = 0 \\ 2 + (1 \div 3) - (a \div 9) = 0 \\ ((6 + 1) \div 3) - (a \div 9) = 0 \\( 7 \div 3) - (a \div 9) = 0 \\ - a \div 9 = - 7 \div 3 \\ a = (7 \times 9) \div 3 \\ a= 7 \times 3 \\ a = 21$

Answer 2

Hope it helps !!